Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.5 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.4.h.b.71.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.823719 | + | 2.70582i | −0.291229 | + | 0.956654i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.64298 | − | 4.45768i | −0.830372 | − | 0.557210i | ||||
\(5\) | 4.71466 | − | 2.72201i | 0.421692 | − | 0.243464i | −0.274109 | − | 0.961699i | \(-0.588383\pi\) |
0.695801 | + | 0.718234i | \(0.255049\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.9358 | + | 12.0873i | 1.13043 | + | 0.652651i | 0.944042 | − | 0.329826i | \(-0.106990\pi\) |
0.186383 | + | 0.982477i | \(0.440323\pi\) | |||||||
\(8\) | 17.5336 | − | 14.3029i | 0.774885 | − | 0.632103i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.48173 | + | 14.9992i | 0.110102 | + | 0.474317i | ||||
\(11\) | −25.3999 | + | 43.9939i | −0.696214 | + | 1.20588i | 0.273556 | + | 0.961856i | \(0.411800\pi\) |
−0.969770 | + | 0.244022i | \(0.921533\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.0883 | + | 43.4542i | 0.535249 | + | 0.927078i | 0.999151 | + | 0.0411921i | \(0.0131156\pi\) |
−0.463902 | + | 0.885886i | \(0.653551\pi\) | |||||||
\(14\) | −49.9512 | + | 46.6920i | −0.953573 | + | 0.891355i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 24.2582 | + | 59.2245i | 0.379035 | + | 0.925382i | ||||
\(17\) | − | 51.7146i | − | 0.737801i | −0.929469 | − | 0.368901i | \(-0.879734\pi\) | ||
0.929469 | − | 0.368901i | \(-0.120266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.9305i | 0.337247i | 0.985681 | + | 0.168624i | \(0.0539322\pi\) | ||||
−0.985681 | + | 0.168624i | \(0.946068\pi\) | |||||||
\(20\) | −43.4533 | − | 2.93419i | −0.485822 | − | 0.0328052i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −98.1174 | − | 104.966i | −0.950850 | − | 1.01722i | ||||
\(23\) | 3.93548 | + | 6.81645i | 0.0356785 | + | 0.0617969i | 0.883313 | − | 0.468783i | \(-0.155307\pi\) |
−0.847635 | + | 0.530580i | \(0.821974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −47.6813 | + | 82.5864i | −0.381450 | + | 0.660691i | ||||
\(26\) | −138.245 | + | 32.0905i | −1.04277 | + | 0.242056i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −85.1946 | − | 173.620i | −0.575010 | − | 1.17183i | ||||
\(29\) | 212.788 | + | 122.853i | 1.36254 | + | 0.786665i | 0.989962 | − | 0.141335i | \(-0.0451395\pi\) |
0.372581 | + | 0.928000i | \(0.378473\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −51.4009 | + | 29.6763i | −0.297802 | + | 0.171936i | −0.641455 | − | 0.767161i | \(-0.721669\pi\) |
0.343653 | + | 0.939097i | \(0.388336\pi\) | |||||||
\(32\) | −180.233 | + | 16.8542i | −0.995656 | + | 0.0931073i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 139.931 | + | 42.5982i | 0.705820 | + | 0.214869i | ||||
\(35\) | 131.607 | 0.635589 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 295.334 | 1.31223 | 0.656116 | − | 0.754660i | \(-0.272198\pi\) | ||||
0.656116 | + | 0.754660i | \(0.272198\pi\) | |||||||
\(38\) | −75.5750 | − | 23.0069i | −0.322629 | − | 0.0982160i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 43.7327 | − | 115.160i | 0.172868 | − | 0.455210i | ||||
\(41\) | 146.833 | − | 84.7741i | 0.559304 | − | 0.322915i | −0.193562 | − | 0.981088i | \(-0.562004\pi\) |
0.752866 | + | 0.658173i | \(0.228671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −284.968 | − | 164.526i | −1.01063 | − | 0.583488i | −0.0992550 | − | 0.995062i | \(-0.531646\pi\) |
−0.911376 | + | 0.411574i | \(0.864979\pi\) | |||||||
\(44\) | 364.841 | − | 179.026i | 1.25004 | − | 0.613390i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −21.6859 | + | 5.03388i | −0.0695088 | + | 0.0161349i | ||||
\(47\) | 47.9742 | − | 83.0938i | 0.148888 | − | 0.257882i | −0.781928 | − | 0.623368i | \(-0.785764\pi\) |
0.930817 | + | 0.365486i | \(0.119097\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 120.704 | + | 209.066i | 0.351908 | + | 0.609522i | ||||
\(50\) | −184.188 | − | 197.045i | −0.520964 | − | 0.557328i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 27.0439 | − | 400.500i | 0.0721213 | − | 1.06807i | ||||
\(53\) | − | 300.751i | − | 0.779459i | −0.920929 | − | 0.389729i | \(-0.872569\pi\) | ||
0.920929 | − | 0.389729i | \(-0.127431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 276.555i | 0.678013i | ||||||||
\(56\) | 539.963 | − | 87.5075i | 1.28849 | − | 0.208816i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −507.697 | + | 474.571i | −1.14938 | + | 1.07438i | ||||
\(59\) | −113.273 | − | 196.195i | −0.249947 | − | 0.432921i | 0.713564 | − | 0.700590i | \(-0.247080\pi\) |
−0.963511 | + | 0.267669i | \(0.913747\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 173.722 | − | 300.896i | 0.364637 | − | 0.631570i | −0.624081 | − | 0.781360i | \(-0.714526\pi\) |
0.988718 | + | 0.149790i | \(0.0478597\pi\) | |||||||
\(62\) | −37.9590 | − | 163.527i | −0.0777548 | − | 0.334966i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 102.857 | − | 501.562i | 0.200892 | − | 0.979613i | ||||
\(65\) | 236.566 | + | 136.581i | 0.451421 | + | 0.260628i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 904.675 | − | 522.314i | 1.64961 | − | 0.952401i | 0.672378 | − | 0.740208i | \(-0.265273\pi\) |
0.977228 | − | 0.212193i | \(-0.0680605\pi\) | |||||||
\(68\) | −230.527 | + | 343.538i | −0.411110 | + | 0.612649i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −108.407 | + | 356.105i | −0.185102 | + | 0.608038i | ||||
\(71\) | −243.524 | −0.407057 | −0.203528 | − | 0.979069i | \(-0.565241\pi\) | ||||
−0.203528 | + | 0.979069i | \(0.565241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1094.68 | −1.75510 | −0.877552 | − | 0.479481i | \(-0.840825\pi\) | ||||
−0.877552 | + | 0.479481i | \(0.840825\pi\) | |||||||
\(74\) | −243.272 | + | 799.122i | −0.382159 | + | 1.25535i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 124.505 | − | 185.542i | 0.187917 | − | 0.280041i | ||||
\(77\) | −1063.53 | + | 614.031i | −1.57404 | + | 0.908770i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −530.679 | − | 306.388i | −0.755773 | − | 0.436346i | 0.0720031 | − | 0.997404i | \(-0.477061\pi\) |
−0.827776 | + | 0.561059i | \(0.810394\pi\) | |||||||
\(80\) | 275.579 | + | 213.192i | 0.385134 | + | 0.297945i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 108.435 | + | 467.135i | 0.146032 | + | 0.629103i | ||||
\(83\) | −283.063 | + | 490.280i | −0.374340 | + | 0.648376i | −0.990228 | − | 0.139458i | \(-0.955464\pi\) |
0.615888 | + | 0.787834i | \(0.288797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −140.768 | − | 243.817i | −0.179628 | − | 0.311125i | ||||
\(86\) | 679.912 | − | 635.549i | 0.852521 | − | 0.796896i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 183.886 | + | 1134.66i | 0.222754 | + | 1.37450i | ||||
\(89\) | 212.529i | 0.253124i | 0.991959 | + | 0.126562i | \(0.0403943\pi\) | ||||
−0.991959 | + | 0.126562i | \(0.959606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1213.00i | 1.39732i | ||||||||
\(92\) | 4.24224 | − | 62.8246i | 0.00480744 | − | 0.0711948i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 185.320 | + | 198.256i | 0.203343 | + | 0.217537i | ||||
\(95\) | 76.0272 | + | 131.683i | 0.0821076 | + | 0.142215i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 234.298 | − | 405.817i | 0.245252 | − | 0.424788i | −0.716951 | − | 0.697124i | \(-0.754463\pi\) |
0.962202 | + | 0.272336i | \(0.0877961\pi\) | |||||||
\(98\) | −665.122 | + | 154.393i | −0.685587 | + | 0.159143i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 684.889 | − | 336.072i | 0.684889 | − | 0.336072i | ||||
\(101\) | −1552.98 | − | 896.613i | −1.52997 | − | 0.883330i | −0.999362 | − | 0.0357140i | \(-0.988629\pi\) |
−0.530610 | − | 0.847616i | \(-0.678037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 119.871 | − | 69.2074i | 0.114672 | − | 0.0662059i | −0.441567 | − | 0.897228i | \(-0.645577\pi\) |
0.556239 | + | 0.831022i | \(0.312244\pi\) | |||||||
\(104\) | 1061.41 | + | 403.076i | 1.00077 | + | 0.380046i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 813.779 | + | 247.734i | 0.745672 | + | 0.227001i | ||||
\(107\) | 771.292 | 0.696857 | 0.348428 | − | 0.937335i | \(-0.386715\pi\) | ||||
0.348428 | + | 0.937335i | \(0.386715\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −275.772 | −0.242332 | −0.121166 | − | 0.992632i | \(-0.538663\pi\) | ||||
−0.121166 | + | 0.992632i | \(0.538663\pi\) | |||||||
\(110\) | −748.310 | − | 227.804i | −0.648623 | − | 0.197457i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −207.998 | + | 1533.13i | −0.175481 | + | 1.29345i | ||||
\(113\) | 542.916 | − | 313.453i | 0.451976 | − | 0.260948i | −0.256689 | − | 0.966494i | \(-0.582631\pi\) |
0.708664 | + | 0.705546i | \(0.249298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 37.1089 | + | 21.4249i | 0.0300907 | + | 0.0173729i | ||||
\(116\) | −865.906 | − | 1764.65i | −0.693080 | − | 1.41245i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 624.173 | − | 144.888i | 0.486947 | − | 0.113034i | ||||
\(119\) | 625.088 | − | 1082.68i | 0.481527 | − | 0.834029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −624.809 | − | 1082.20i | −0.469428 | − | 0.813073i | ||||
\(122\) | 671.073 | + | 717.916i | 0.498001 | + | 0.532762i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 473.742 | + | 31.9895i | 0.343091 | + | 0.0231673i | ||||
\(125\) | 1199.66i | 0.858406i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 71.3408i | 0.0498463i | 0.999689 | + | 0.0249231i | \(0.00793410\pi\) | ||||
−0.999689 | + | 0.0249231i | \(0.992066\pi\) | |||||||
\(128\) | 1272.41 | + | 691.458i | 0.878645 | + | 0.477475i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −564.428 | + | 527.601i | −0.380797 | + | 0.355951i | ||||
\(131\) | 358.903 | + | 621.638i | 0.239370 | + | 0.414601i | 0.960534 | − | 0.278164i | \(-0.0897258\pi\) |
−0.721164 | + | 0.692765i | \(0.756392\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −337.604 | + | 584.747i | −0.220105 | + | 0.381233i | ||||
\(134\) | 668.093 | + | 2878.13i | 0.430705 | + | 1.85547i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −739.666 | − | 906.744i | −0.466366 | − | 0.571711i | ||||
\(137\) | −190.925 | − | 110.231i | −0.119065 | − | 0.0687420i | 0.439285 | − | 0.898348i | \(-0.355232\pi\) |
−0.558350 | + | 0.829606i | \(0.688565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1214.70 | − | 701.309i | 0.741222 | − | 0.427945i | −0.0812916 | − | 0.996690i | \(-0.525905\pi\) |
0.822513 | + | 0.568746i | \(0.192571\pi\) | |||||||
\(140\) | −874.261 | − | 586.661i | −0.527775 | − | 0.354156i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 200.596 | − | 658.934i | 0.118547 | − | 0.389412i | ||||
\(143\) | −2548.96 | −1.49059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1337.63 | 0.766099 | ||||||||
\(146\) | 901.708 | − | 2962.01i | 0.511136 | − | 1.67903i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1961.90 | − | 1316.50i | −1.08964 | − | 0.731188i | ||||
\(149\) | 1289.36 | − | 744.413i | 0.708917 | − | 0.409293i | −0.101743 | − | 0.994811i | \(-0.532442\pi\) |
0.810660 | + | 0.585517i | \(0.199109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1704.17 | − | 983.903i | −0.918433 | − | 0.530257i | −0.0352979 | − | 0.999377i | \(-0.511238\pi\) |
−0.883135 | + | 0.469120i | \(0.844571\pi\) | |||||||
\(152\) | 399.486 | + | 489.723i | 0.213175 | + | 0.261328i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −785.408 | − | 3383.52i | −0.410974 | − | 1.77047i | ||||
\(155\) | −161.559 | + | 279.828i | −0.0837206 | + | 0.145008i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 564.122 | + | 977.088i | 0.286763 | + | 0.496689i | 0.973035 | − | 0.230656i | \(-0.0740874\pi\) |
−0.686272 | + | 0.727345i | \(0.740754\pi\) | |||||||
\(158\) | 1266.16 | − | 1183.55i | 0.637534 | − | 0.595937i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −803.861 | + | 570.059i | −0.397192 | + | 0.281669i | ||||
\(161\) | 190.277i | 0.0931424i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1940.05i | − | 0.932250i | −0.884719 | − | 0.466125i | \(-0.845650\pi\) | ||
0.884719 | − | 0.466125i | \(-0.154350\pi\) | |||||||
\(164\) | −1353.30 | − | 91.3821i | −0.644362 | − | 0.0435106i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1093.45 | − | 1169.77i | −0.511252 | − | 0.546939i | ||||
\(167\) | −1242.52 | − | 2152.11i | −0.575743 | − | 0.997217i | −0.995960 | − | 0.0897933i | \(-0.971379\pi\) |
0.420217 | − | 0.907424i | \(-0.361954\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −160.344 | + | 277.723i | −0.0729830 | + | 0.126410i | ||||
\(170\) | 775.678 | − | 180.056i | 0.349952 | − | 0.0812334i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1159.63 | + | 2363.24i | 0.514075 | + | 1.04765i | ||||
\(173\) | 2492.67 | + | 1439.15i | 1.09546 | + | 0.632464i | 0.935025 | − | 0.354583i | \(-0.115377\pi\) |
0.160435 | + | 0.987046i | \(0.448710\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1996.49 | + | 1152.67i | −0.862402 | + | 0.497908i | ||||
\(176\) | −3221.67 | − | 437.081i | −1.37979 | − | 0.187194i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −575.067 | − | 175.064i | −0.242152 | − | 0.0737170i | ||||
\(179\) | 2965.78 | 1.23840 | 0.619198 | − | 0.785235i | \(-0.287458\pi\) | ||||
0.619198 | + | 0.785235i | \(0.287458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1250.55 | 0.513551 | 0.256776 | − | 0.966471i | \(-0.417340\pi\) | ||||
0.256776 | + | 0.966471i | \(0.417340\pi\) | |||||||
\(182\) | −3282.15 | − | 999.167i | −1.33675 | − | 0.406941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 166.498 | + | 63.2286i | 0.0667087 | + | 0.0253330i | ||||
\(185\) | 1392.40 | − | 803.902i | 0.553358 | − | 0.319482i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2275.12 | + | 1313.54i | 0.889698 | + | 0.513668i | ||||
\(188\) | −689.097 | + | 338.136i | −0.267327 | + | 0.131176i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −418.936 | + | 97.2465i | −0.159962 | + | 0.0371316i | ||||
\(191\) | 387.763 | − | 671.626i | 0.146898 | − | 0.254435i | −0.783181 | − | 0.621793i | \(-0.786404\pi\) |
0.930080 | + | 0.367358i | \(0.119738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2185.71 | + | 3785.76i | 0.815185 | + | 1.41194i | 0.909195 | + | 0.416370i | \(0.136698\pi\) |
−0.0940101 | + | 0.995571i | \(0.529969\pi\) | |||||||
\(194\) | 905.073 | + | 968.249i | 0.334951 | + | 0.358331i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 130.113 | − | 1926.88i | 0.0474173 | − | 0.702216i | ||||
\(197\) | − | 1648.60i | − | 0.596233i | −0.954530 | − | 0.298116i | \(-0.903642\pi\) | ||
0.954530 | − | 0.298116i | \(-0.0963584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2946.42i | 1.04958i | 0.851232 | + | 0.524790i | \(0.175856\pi\) | ||||
−0.851232 | + | 0.524790i | \(0.824144\pi\) | |||||||
\(200\) | 345.195 | + | 2130.02i | 0.122045 | + | 0.753075i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3705.30 | − | 3463.53i | 1.29061 | − | 1.20640i | ||||
\(203\) | 2969.92 | + | 5144.05i | 1.02684 | + | 1.77853i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 461.513 | − | 799.363i | 0.157236 | − | 0.272341i | ||||
\(206\) | 88.5233 | + | 381.356i | 0.0299403 | + | 0.128982i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1964.95 | + | 2539.96i | −0.655024 | + | 0.846705i | ||||
\(209\) | −1228.77 | − | 709.432i | −0.406679 | − | 0.234796i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −477.089 | + | 275.447i | −0.155659 | + | 0.0898700i | −0.575806 | − | 0.817586i | \(-0.695312\pi\) |
0.420147 | + | 0.907456i | \(0.361979\pi\) | |||||||
\(212\) | −1340.65 | + | 1997.88i | −0.434322 | + | 0.647241i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −635.328 | + | 2086.98i | −0.202945 | + | 0.666650i | ||||
\(215\) | −1791.37 | −0.568234 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1434.82 | −0.448857 | ||||||||
\(218\) | 227.159 | − | 746.192i | 0.0705741 | − | 0.231828i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1232.79 | − | 1837.15i | 0.377795 | − | 0.563003i | ||||
\(221\) | 2247.21 | − | 1297.43i | 0.684000 | − | 0.394907i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1564.82 | − | 903.449i | −0.469902 | − | 0.271298i | 0.246297 | − | 0.969194i | \(-0.420786\pi\) |
−0.716199 | + | 0.697897i | \(0.754120\pi\) | |||||||
\(224\) | −3977.04 | − | 1825.67i | −1.18628 | − | 0.544565i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 400.938 | + | 1727.23i | 0.118009 | + | 0.508380i | ||||
\(227\) | −752.796 | + | 1303.88i | −0.220109 | + | 0.381241i | −0.954841 | − | 0.297117i | \(-0.903975\pi\) |
0.734732 | + | 0.678358i | \(0.237308\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −767.015 | − | 1328.51i | −0.221335 | − | 0.383364i | 0.733878 | − | 0.679281i | \(-0.237708\pi\) |
−0.955214 | + | 0.295917i | \(0.904375\pi\) | |||||||
\(230\) | −88.5392 | + | 82.7622i | −0.0253831 | + | 0.0237269i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5488.10 | − | 889.413i | 1.55307 | − | 0.251693i | ||||
\(233\) | 1257.04i | 0.353440i | 0.984261 | + | 0.176720i | \(0.0565487\pi\) | ||||
−0.984261 | + | 0.176720i | \(0.943451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 522.346i | − | 0.144996i | ||||||
\(236\) | −122.102 | + | 1808.25i | −0.0336787 | + | 0.498759i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2414.66 | + | 2583.21i | 0.657643 | + | 0.703548i | ||||
\(239\) | −916.982 | − | 1588.26i | −0.248178 | − | 0.429858i | 0.714842 | − | 0.699286i | \(-0.246499\pi\) |
−0.963020 | + | 0.269428i | \(0.913165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −358.771 | + | 621.410i | −0.0958941 | + | 0.166094i | −0.909981 | − | 0.414649i | \(-0.863904\pi\) |
0.814087 | + | 0.580743i | \(0.197238\pi\) | |||||||
\(242\) | 3442.91 | − | 799.194i | 0.914540 | − | 0.212290i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2495.33 | + | 1224.45i | −0.654701 | + | 0.321259i | ||||
\(245\) | 1138.16 | + | 657.117i | 0.296794 | + | 0.171354i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1213.70 | + | 700.728i | −0.312655 | + | 0.180511i | ||||
\(248\) | −476.788 | + | 1255.51i | −0.122081 | + | 0.321472i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3246.07 | − | 988.182i | −0.821198 | − | 0.249992i | ||||
\(251\) | −1053.84 | −0.265010 | −0.132505 | − | 0.991182i | \(-0.542302\pi\) | ||||
−0.132505 | + | 0.991182i | \(0.542302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −399.843 | −0.0993594 | ||||||||
\(254\) | −193.036 | − | 58.7648i | −0.0476856 | − | 0.0145167i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2919.08 | + | 2873.36i | −0.712665 | + | 0.701504i | ||||
\(257\) | −5985.55 | + | 3455.76i | −1.45280 | + | 0.838772i | −0.998639 | − | 0.0521496i | \(-0.983393\pi\) |
−0.454157 | + | 0.890922i | \(0.650059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6183.04 | + | 3569.78i | 1.48338 | + | 0.856430i | ||||
\(260\) | −962.665 | − | 1961.84i | −0.229623 | − | 0.467954i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1977.68 | + | 459.073i | −0.466341 | + | 0.108251i | ||||
\(263\) | −1325.23 | + | 2295.36i | −0.310712 | + | 0.538168i | −0.978517 | − | 0.206168i | \(-0.933901\pi\) |
0.667805 | + | 0.744336i | \(0.267234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −818.648 | − | 1417.94i | −0.189770 | − | 0.328692i | ||||
\(266\) | −1304.13 | − | 1395.16i | −0.300607 | − | 0.321590i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8338.04 | − | 563.027i | −1.90047 | − | 0.128330i | ||||
\(269\) | − | 2386.16i | − | 0.540843i | −0.962742 | − | 0.270422i | \(-0.912837\pi\) | ||
0.962742 | − | 0.270422i | \(-0.0871631\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4287.45i | − | 0.961048i | −0.876982 | − | 0.480524i | \(-0.840446\pi\) | ||
0.876982 | − | 0.480524i | \(-0.159554\pi\) | |||||||
\(272\) | 3062.77 | − | 1254.50i | 0.682748 | − | 0.279652i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 455.534 | − | 425.811i | 0.100437 | − | 0.0938839i | ||||
\(275\) | −2422.20 | − | 4195.37i | −0.531142 | − | 0.919965i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2416.58 | + | 4185.64i | −0.524181 | + | 0.907909i | 0.475422 | + | 0.879758i | \(0.342295\pi\) |
−0.999604 | + | 0.0281511i | \(0.991038\pi\) | |||||||
\(278\) | 897.046 | + | 3864.46i | 0.193530 | + | 0.833722i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2307.55 | − | 1882.35i | 0.492508 | − | 0.401758i | ||||
\(281\) | −1501.29 | − | 866.770i | −0.318717 | − | 0.184011i | 0.332104 | − | 0.943243i | \(-0.392242\pi\) |
−0.650821 | + | 0.759232i | \(0.725575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3227.63 | − | 1863.47i | 0.677960 | − | 0.391420i | −0.121126 | − | 0.992637i | \(-0.538650\pi\) |
0.799086 | + | 0.601217i | \(0.205317\pi\) | |||||||
\(284\) | 1617.73 | + | 1085.55i | 0.338009 | + | 0.226816i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2099.62 | − | 6897.03i | 0.434103 | − | 1.42598i | ||||
\(287\) | 4098.75 | 0.843003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2238.61 | 0.455649 | ||||||||
\(290\) | −1101.83 | + | 3619.40i | −0.223110 | + | 0.732891i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7271.93 | + | 4879.73i | 1.45739 | + | 0.977961i | ||||
\(293\) | −5604.61 | + | 3235.82i | −1.11749 | + | 0.645183i | −0.940759 | − | 0.339076i | \(-0.889886\pi\) |
−0.176731 | + | 0.984259i | \(0.556552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1068.09 | − | 616.661i | −0.210802 | − | 0.121706i | ||||
\(296\) | 5178.28 | − | 4224.12i | 1.01683 | − | 0.829466i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 952.180 | + | 4101.97i | 0.185095 | + | 0.797386i | ||||
\(299\) | −197.469 | + | 342.026i | −0.0381937 | + | 0.0661534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3977.34 | − | 6888.96i | −0.761629 | − | 1.31918i | ||||
\(302\) | 4066.02 | − | 3800.72i | 0.774746 | − | 0.724196i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1654.17 | + | 677.545i | −0.312083 | + | 0.127828i | ||||
\(305\) | − | 1891.50i | − | 0.355104i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7858.86i | − | 1.46101i | −0.682909 | − | 0.730503i | \(-0.739285\pi\) | ||
0.682909 | − | 0.730503i | \(-0.260715\pi\) | |||||||
\(308\) | 9802.17 | + | 661.893i | 1.81341 | + | 0.122451i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −624.086 | − | 667.648i | −0.114341 | − | 0.122322i | ||||
\(311\) | −3745.08 | − | 6486.66i | −0.682842 | − | 1.18272i | −0.974110 | − | 0.226075i | \(-0.927410\pi\) |
0.291268 | − | 0.956642i | \(-0.405923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4304.38 | − | 7455.41i | 0.777310 | − | 1.34634i | −0.156176 | − | 0.987729i | \(-0.549917\pi\) |
0.933487 | − | 0.358612i | \(-0.116750\pi\) | |||||||
\(314\) | −3108.51 | + | 721.570i | −0.558672 | + | 0.129683i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2159.51 | + | 4400.92i | 0.384437 | + | 0.783453i | ||||
\(317\) | 4705.42 | + | 2716.67i | 0.833699 | + | 0.481336i | 0.855117 | − | 0.518434i | \(-0.173485\pi\) |
−0.0214185 | + | 0.999771i | \(0.506818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10809.6 | + | 6240.92i | −1.89724 | + | 1.09537i | ||||
\(320\) | −880.323 | − | 2644.67i | −0.153786 | − | 0.462006i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −514.856 | − | 156.735i | −0.0891050 | − | 0.0271257i | ||||
\(323\) | 1444.41 | 0.248821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4784.97 | −0.816684 | ||||||||
\(326\) | 5249.44 | + | 1598.06i | 0.891840 | + | 0.271498i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1362.01 | − | 3586.53i | 0.229281 | − | 0.603759i | ||||
\(329\) | 2008.75 | − | 1159.75i | 0.336615 | − | 0.194344i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1367.21 | + | 789.359i | 0.227035 | + | 0.131079i | 0.609204 | − | 0.793014i | \(-0.291489\pi\) |
−0.382168 | + | 0.924093i | \(0.624823\pi\) | |||||||
\(332\) | 4065.89 | − | 1995.11i | 0.672122 | − | 0.329807i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6846.72 | − | 1589.31i | 1.12166 | − | 0.260369i | ||||
\(335\) | 2843.49 | − | 4925.07i | 0.463751 | − | 0.803240i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3400.38 | − | 5889.62i | −0.549645 | − | 0.952013i | −0.998299 | − | 0.0583070i | \(-0.981430\pi\) |
0.448654 | − | 0.893706i | \(-0.351904\pi\) | |||||||
\(338\) | −619.393 | − | 662.628i | −0.0996761 | − | 0.106634i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −151.740 | + | 2247.17i | −0.0242037 | + | 0.358440i | ||||
\(341\) | − | 3015.10i | − | 0.478818i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2455.93i | − | 0.386611i | ||||||
\(344\) | −7349.71 | + | 1191.11i | −1.15195 | + | 0.186687i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5947.34 | + | 5559.29i | −0.924078 | + | 0.863784i | ||||
\(347\) | 6228.10 | + | 10787.4i | 0.963522 | + | 1.66887i | 0.713535 | + | 0.700620i | \(0.247093\pi\) |
0.249987 | + | 0.968249i | \(0.419573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −910.729 | + | 1577.43i | −0.139685 | + | 0.241942i | −0.927378 | − | 0.374127i | \(-0.877942\pi\) |
0.787692 | + | 0.616069i | \(0.211276\pi\) | |||||||
\(350\) | −1474.39 | − | 6351.63i | −0.225169 | − | 0.970025i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3836.42 | − | 8357.25i | 0.580914 | − | 1.26546i | ||||
\(353\) | −6019.52 | − | 3475.37i | −0.907611 | − | 0.524010i | −0.0279495 | − | 0.999609i | \(-0.508898\pi\) |
−0.879662 | + | 0.475600i | \(0.842231\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1148.14 | + | 662.877i | −0.171653 | + | 0.0991038i | ||||
\(356\) | 947.387 | − | 1411.83i | 0.141043 | − | 0.210187i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2442.97 | + | 8024.88i | −0.360656 | + | 1.18472i | ||||
\(359\) | 318.743 | 0.0468597 | 0.0234298 | − | 0.999725i | \(-0.492541\pi\) | ||||
0.0234298 | + | 0.999725i | \(0.492541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6078.89 | 0.886264 | ||||||||
\(362\) | −1030.10 | + | 3383.77i | −0.149561 | + | 0.491290i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5407.14 | − | 8057.90i | 0.778602 | − | 1.16030i | ||||
\(365\) | −5161.05 | + | 2979.73i | −0.740114 | + | 0.427305i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5425.21 | + | 3132.25i | 0.771645 | + | 0.445510i | 0.833461 | − | 0.552578i | \(-0.186356\pi\) |
−0.0618160 | + | 0.998088i | \(0.519689\pi\) | |||||||
\(368\) | −308.233 | + | 398.432i | −0.0436624 | + | 0.0564394i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1028.27 | + | 4429.78i | 0.144479 | + | 0.622414i | ||||
\(371\) | 3635.26 | − | 6296.45i | 0.508715 | − | 0.881120i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6066.19 | + | 10506.9i | 0.842078 | + | 1.45852i | 0.888135 | + | 0.459583i | \(0.152001\pi\) |
−0.0460564 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(374\) | −5428.28 | + | 5074.10i | −0.750508 | + | 0.701538i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −347.316 | − | 2143.10i | −0.0476368 | − | 0.293942i | ||||
\(377\) | 12328.7i | 1.68425i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1928.72i | 0.261402i | 0.991422 | + | 0.130701i | \(0.0417229\pi\) | ||||
−0.991422 | + | 0.130701i | \(0.958277\pi\) | |||||||
\(380\) | 81.9533 | − | 1213.67i | 0.0110635 | − | 0.163842i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1497.89 | + | 1602.45i | 0.200625 | + | 0.214630i | ||||
\(383\) | −2974.93 | − | 5152.73i | −0.396898 | − | 0.687448i | 0.596443 | − | 0.802655i | \(-0.296580\pi\) |
−0.993341 | + | 0.115208i | \(0.963247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3342.80 | + | 5789.90i | −0.442506 | + | 0.766443i | ||||
\(386\) | −12044.0 | + | 2795.74i | −1.58814 | + | 0.368652i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3365.44 | + | 1651.40i | −0.440346 | + | 0.216076i | ||||
\(389\) | −2023.11 | − | 1168.05i | −0.263691 | − | 0.152242i | 0.362326 | − | 0.932051i | \(-0.381983\pi\) |
−0.626017 | + | 0.779809i | \(0.715316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 352.510 | − | 203.522i | 0.0455938 | − | 0.0263236i | ||||
\(392\) | 5106.63 | + | 1939.27i | 0.657968 | + | 0.249867i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4460.82 | + | 1357.98i | 0.570388 | + | 0.173640i | ||||
\(395\) | −3335.97 | −0.424938 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6080.16 | −0.768652 | −0.384326 | − | 0.923198i | \(-0.625566\pi\) | ||||
−0.384326 | + | 0.923198i | \(0.625566\pi\) | |||||||
\(398\) | −7972.51 | − | 2427.02i | −1.00408 | − | 0.305668i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6047.80 | − | 820.499i | −0.755975 | − | 0.102562i | ||||
\(401\) | 11997.7 | − | 6926.90i | 1.49411 | − | 0.862626i | 0.494135 | − | 0.869385i | \(-0.335485\pi\) |
0.999977 | + | 0.00675957i | \(0.00215165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2579.12 | − | 1489.05i | −0.318797 | − | 0.184057i | ||||
\(404\) | 6319.59 | + | 12878.9i | 0.778246 | + | 1.58601i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16365.3 | + | 3798.83i | −2.00048 | + | 0.464367i | ||||
\(407\) | −7501.45 | + | 12992.9i | −0.913594 | + | 1.58239i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 135.435 | + | 234.581i | 0.0163737 | + | 0.0283601i | 0.874096 | − | 0.485753i | \(-0.161455\pi\) |
−0.857722 | + | 0.514113i | \(0.828121\pi\) | |||||||
\(410\) | 1782.78 | + | 1907.22i | 0.214745 | + | 0.229734i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1104.80 | − | 74.6019i | −0.132111 | − | 0.00892081i | ||||
\(413\) | − | 5476.64i | − | 0.652513i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3082.01i | 0.364553i | ||||||||
\(416\) | −5254.12 | − | 7409.03i | −0.619242 | − | 0.873216i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2931.76 | − | 2740.47i | 0.343055 | − | 0.320672i | ||||
\(419\) | 3950.75 | + | 6842.90i | 0.460637 | + | 0.797846i | 0.998993 | − | 0.0448712i | \(-0.0142877\pi\) |
−0.538356 | + | 0.842718i | \(0.680954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3331.91 | − | 5771.04i | 0.385718 | − | 0.668083i | −0.606150 | − | 0.795350i | \(-0.707287\pi\) |
0.991869 | + | 0.127267i | \(0.0406204\pi\) | |||||||
\(422\) | −352.325 | − | 1517.81i | −0.0406420 | − | 0.175085i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4301.60 | − | 5273.26i | −0.492698 | − | 0.603991i | ||||
\(425\) | 4270.92 | + | 2465.82i | 0.487459 | + | 0.281435i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7274.02 | − | 4199.66i | 0.824390 | − | 0.475962i | ||||
\(428\) | −5123.68 | − | 3438.17i | −0.578650 | − | 0.388295i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1475.58 | − | 4847.13i | 0.165486 | − | 0.543603i | ||||
\(431\) | −14773.0 | −1.65102 | −0.825509 | − | 0.564388i | \(-0.809112\pi\) | ||||
−0.825509 | + | 0.564388i | \(0.809112\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2372.81 | −0.263349 | −0.131674 | − | 0.991293i | \(-0.542035\pi\) | ||||
−0.131674 | + | 0.991293i | \(0.542035\pi\) | |||||||
\(434\) | 1181.89 | − | 3882.38i | 0.130720 | − | 0.429401i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1831.95 | + | 1229.30i | 0.201226 | + | 0.135030i | ||||
\(437\) | −190.387 | + | 109.920i | −0.0208408 | + | 0.0120325i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2509.56 | + | 1448.89i | 0.272835 | + | 0.157522i | 0.630175 | − | 0.776453i | \(-0.282983\pi\) |
−0.357340 | + | 0.933974i | \(0.616316\pi\) | |||||||
\(440\) | 3955.53 | + | 4849.02i | 0.428574 | + | 0.525382i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1659.54 | + | 7149.28i | 0.178589 | + | 0.769359i | ||||
\(443\) | −3932.06 | + | 6810.53i | −0.421711 | + | 0.730425i | −0.996107 | − | 0.0881526i | \(-0.971904\pi\) |
0.574396 | + | 0.818578i | \(0.305237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 578.508 | + | 1002.00i | 0.0616267 | + | 0.106741i | ||||
\(446\) | 3733.55 | − | 3489.94i | 0.396387 | − | 0.370523i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8215.90 | − | 9257.33i | 0.866439 | − | 0.976267i | ||||
\(449\) | − | 1335.91i | − | 0.140413i | −0.997532 | − | 0.0702064i | \(-0.977634\pi\) | ||
0.997532 | − | 0.0702064i | \(-0.0223658\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8613.02i | 0.899271i | ||||||||
\(452\) | −5003.85 | − | 337.886i | −0.520711 | − | 0.0351611i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2907.98 | − | 3110.97i | −0.300613 | − | 0.321597i | ||||
\(455\) | 3301.79 | + | 5718.87i | 0.340198 | + | 0.589241i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8696.49 | + | 15062.8i | −0.890164 | + | 1.54181i | −0.0504849 | + | 0.998725i | \(0.516077\pi\) |
−0.839679 | + | 0.543084i | \(0.817257\pi\) | |||||||
\(458\) | 4226.52 | − | 981.091i | 0.431206 | − | 0.100095i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −151.009 | − | 307.744i | −0.0153061 | − | 0.0311927i | ||||
\(461\) | 1933.14 | + | 1116.10i | 0.195304 | + | 0.112759i | 0.594463 | − | 0.804123i | \(-0.297365\pi\) |
−0.399159 | + | 0.916882i | \(0.630698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3435.96 | − | 1983.75i | 0.344887 | − | 0.199121i | −0.317544 | − | 0.948244i | \(-0.602858\pi\) |
0.662431 | + | 0.749123i | \(0.269525\pi\) | |||||||
\(464\) | −2114.06 | + | 15582.5i | −0.211514 | + | 1.55905i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3401.33 | − | 1035.45i | −0.338120 | − | 0.102932i | ||||
\(467\) | 8810.21 | 0.872993 | 0.436497 | − | 0.899706i | \(-0.356219\pi\) | ||||
0.436497 | + | 0.899706i | \(0.356219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25253.4 | 2.48634 | ||||||||
\(470\) | 1413.38 | + | 430.266i | 0.138711 | + | 0.0422270i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4792.23 | − | 1819.88i | −0.467331 | − | 0.177472i | ||||
\(473\) | 14476.3 | − | 8357.89i | 1.40723 | − | 0.812466i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2306.68 | − | 1331.76i | −0.222816 | − | 0.128643i | ||||
\(476\) | −8978.70 | + | 4405.80i | −0.864576 | + | 0.424243i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5052.89 | − | 1172.91i | 0.483502 | − | 0.112234i | ||||
\(479\) | 9734.00 | − | 16859.8i | 0.928513 | − | 1.60823i | 0.142702 | − | 0.989766i | \(-0.454421\pi\) |
0.785811 | − | 0.618466i | \(-0.212246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7409.42 | + | 12833.5i | 0.702371 | + | 1.21654i | ||||
\(482\) | −1385.90 | − | 1482.64i | −0.130967 | − | 0.140109i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −673.511 | + | 9974.23i | −0.0632524 | + | 0.936723i | ||||
\(485\) | − | 2551.05i | − | 0.238840i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5226.26i | 0.486293i | 0.969990 | + | 0.243146i | \(0.0781795\pi\) | ||||
−0.969990 | + | 0.243146i | \(0.921820\pi\) | |||||||
\(488\) | −1257.69 | − | 7760.52i | −0.116666 | − | 0.719882i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2715.57 | + | 2538.38i | −0.250361 | + | 0.234025i | ||||
\(491\) | −4793.56 | − | 8302.69i | −0.440591 | − | 0.763127i | 0.557142 | − | 0.830417i | \(-0.311898\pi\) |
−0.997733 | + | 0.0672904i | \(0.978565\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6353.30 | − | 11004.2i | 0.580402 | − | 1.00529i | ||||
\(494\) | −896.303 | − | 3861.25i | −0.0816327 | − | 0.351672i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3004.46 | − | 2324.29i | −0.271984 | − | 0.210411i | ||||
\(497\) | −5098.37 | − | 2943.55i | −0.460147 | − | 0.265666i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2085.65 | − | 1204.15i | 0.187108 | − | 0.108027i | −0.403520 | − | 0.914971i | \(-0.632213\pi\) |
0.590628 | + | 0.806944i | \(0.298880\pi\) | |||||||
\(500\) | 5347.69 | − | 7969.31i | 0.478312 | − | 0.712797i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 868.064 | − | 2851.49i | 0.0771785 | − | 0.253523i | ||||
\(503\) | 17192.1 | 1.52397 | 0.761985 | − | 0.647595i | \(-0.224225\pi\) | ||||
0.761985 | + | 0.647595i | \(0.224225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9762.37 | −0.860237 | ||||||||
\(506\) | 329.358 | − | 1081.91i | 0.0289363 | − | 0.0950525i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 318.014 | − | 473.915i | 0.0277748 | − | 0.0413909i | ||||
\(509\) | 2562.66 | − | 1479.55i | 0.223159 | − | 0.128841i | −0.384253 | − | 0.923228i | \(-0.625541\pi\) |
0.607412 | + | 0.794387i | \(0.292208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22918.0 | − | 13231.7i | −1.98401 | − | 1.14547i | ||||
\(512\) | −5370.32 | − | 10265.4i | −0.463548 | − | 0.886072i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4420.27 | − | 19042.4i | −0.379319 | − | 1.63410i | ||||
\(515\) | 376.767 | − | 652.579i | 0.0322375 | − | 0.0558370i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2437.08 | + | 4221.14i | 0.207316 | + | 0.359083i | ||||
\(518\) | −14752.3 | + | 13789.7i | −1.25131 | + | 1.16966i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6101.36 | − | 988.798i | 0.514543 | − | 0.0833878i | ||||
\(521\) | 12490.4i | 1.05032i | 0.851004 | + | 0.525159i | \(0.175994\pi\) | ||||
−0.851004 | + | 0.525159i | \(0.824006\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13273.1i | 1.10974i | 0.831939 | + | 0.554868i | \(0.187231\pi\) | ||||
−0.831939 | + | 0.554868i | \(0.812769\pi\) | |||||||
\(524\) | 386.878 | − | 5729.40i | 0.0322535 | − | 0.477652i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5119.24 | − | 5476.57i | −0.424352 | − | 0.453973i | ||||
\(527\) | 1534.70 | + | 2658.17i | 0.126855 | + | 0.219719i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6052.52 | − | 10483.3i | 0.497454 | − | 0.861616i | ||||
\(530\) | 4511.03 | − | 1047.13i | 0.369711 | − | 0.0858200i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4849.30 | − | 2379.53i | 0.395195 | − | 0.193920i | ||||
\(533\) | 7367.58 | + | 4253.68i | 0.598734 | + | 0.345679i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3636.38 | − | 2099.47i | 0.293859 | − | 0.169660i | ||||
\(536\) | 8391.65 | − | 22097.5i | 0.676239 | − | 1.78072i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6456.53 | + | 1965.53i | 0.517400 | + | 0.157509i | ||||
\(539\) | −12263.5 | −0.980012 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12385.8 | −0.984302 | −0.492151 | − | 0.870510i | \(-0.663789\pi\) | ||||
−0.492151 | + | 0.870510i | \(0.663789\pi\) | |||||||
\(542\) | 11601.1 | + | 3531.65i | 0.919390 | + | 0.279885i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 871.609 | + | 9320.67i | 0.0686947 | + | 0.734596i | ||||
\(545\) | −1300.17 | + | 750.656i | −0.102190 | + | 0.0589992i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15941.6 | − | 9203.89i | −1.24609 | − | 0.719433i | −0.275766 | − | 0.961225i | \(-0.588932\pi\) |
−0.970328 | + | 0.241792i | \(0.922265\pi\) | |||||||
\(548\) | 776.939 | + | 1583.34i | 0.0605642 | + | 0.123425i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13347.2 | − | 3098.24i | 1.03477 | − | 0.240199i | ||||
\(551\) | −3431.35 | + | 5943.28i | −0.265300 | + | 0.459514i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7406.78 | − | 12828.9i | −0.569563 | − | 0.986512i | ||||
\(554\) | −9335.03 | − | 9986.63i | −0.715898 | − | 0.765869i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11195.5 | − | 755.975i | −0.853944 | − | 0.0576627i | ||||
\(557\) | 13864.9i | 1.05472i | 0.849643 | + | 0.527358i | \(0.176817\pi\) | ||||
−0.849643 | + | 0.527358i | \(0.823183\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16510.7i | − | 1.24925i | ||||||
\(560\) | 3192.55 | + | 7794.35i | 0.240910 | + | 0.588163i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3581.97 | − | 3348.25i | 0.268854 | − | 0.251312i | ||||
\(563\) | −7442.77 | − | 12891.3i | −0.557150 | − | 0.965012i | −0.997733 | − | 0.0672999i | \(-0.978562\pi\) |
0.440583 | − | 0.897712i | \(-0.354772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1706.44 | − | 2955.65i | 0.127063 | − | 0.220080i | ||||
\(566\) | 2383.57 | + | 10268.4i | 0.177012 | + | 0.762566i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4269.87 | + | 3483.09i | −0.315422 | + | 0.257302i | ||||
\(569\) | −5893.56 | − | 3402.65i | −0.434219 | − | 0.250697i | 0.266923 | − | 0.963718i | \(-0.413993\pi\) |
−0.701142 | + | 0.713021i | \(0.747326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7163.27 | + | 4135.72i | −0.524998 | + | 0.303108i | −0.738977 | − | 0.673731i | \(-0.764691\pi\) |
0.213979 | + | 0.976838i | \(0.431357\pi\) | |||||||
\(572\) | 16932.7 | + | 11362.4i | 1.23775 | + | 0.830572i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3376.22 | + | 11090.5i | −0.245506 | + | 0.806461i | ||||
\(575\) | −750.595 | −0.0544382 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12153.3 | −0.876863 | −0.438432 | − | 0.898765i | \(-0.644466\pi\) | ||||
−0.438432 | + | 0.898765i | \(0.644466\pi\) | |||||||
\(578\) | −1843.98 | + | 6057.27i | −0.132698 | + | 0.435899i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8885.86 | − | 5962.73i | −0.636147 | − | 0.426878i | ||||
\(581\) | −11852.3 | + | 6842.92i | −0.846327 | + | 0.488627i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13231.2 | + | 7639.04i | 0.939932 | + | 0.542670i | ||||
\(584\) | −19193.7 | + | 15657.0i | −1.36000 | + | 1.10941i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4138.95 | − | 17830.5i | −0.291772 | − | 1.25695i | ||||
\(587\) | 7165.79 | − | 12411.5i | 0.503856 | − | 0.872705i | −0.496134 | − | 0.868246i | \(-0.665247\pi\) |
0.999990 | − | 0.00445871i | \(-0.00141926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −828.874 | − | 1435.65i | −0.0579850 | − | 0.100433i | ||||
\(590\) | 2548.38 | − | 2382.10i | 0.177822 | − | 0.166220i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7164.28 | + | 17491.0i | 0.497382 | + | 1.21432i | ||||
\(593\) | − | 17892.9i | − | 1.23908i | −0.784966 | − | 0.619539i | \(-0.787319\pi\) | ||
0.784966 | − | 0.619539i | \(-0.212681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6805.99i | − | 0.468938i | ||||||
\(596\) | −11883.5 | − | 802.438i | −0.816727 | − | 0.0551496i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −762.804 | − | 816.049i | −0.0521628 | − | 0.0558039i | ||||
\(599\) | 5989.96 | + | 10374.9i | 0.408586 | + | 0.707692i | 0.994732 | − | 0.102514i | \(-0.0326886\pi\) |
−0.586145 | + | 0.810206i | \(0.699355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1473.48 | + | 2552.14i | −0.100007 | + | 0.173218i | −0.911687 | − | 0.410885i | \(-0.865220\pi\) |
0.811680 | + | 0.584102i | \(0.198553\pi\) | |||||||
\(602\) | 21916.5 | − | 5087.43i | 1.48381 | − | 0.344432i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6934.83 | + | 14132.7i | 0.467176 | + | 0.952070i | ||||
\(605\) | −5891.53 | − | 3401.48i | −0.395909 | − | 0.228578i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22272.8 | − | 12859.2i | 1.48933 | − | 0.859866i | 0.489406 | − | 0.872056i | \(-0.337214\pi\) |
0.999926 | + | 0.0121903i | \(0.00388040\pi\) | |||||||
\(608\) | −470.747 | − | 5034.00i | −0.0314002 | − | 0.335782i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5118.06 | + | 1558.06i | 0.339712 | + | 0.103417i | ||||
\(611\) | 4814.36 | 0.318770 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1851.43 | −0.121988 | −0.0609938 | − | 0.998138i | \(-0.519427\pi\) | ||||
−0.0609938 | + | 0.998138i | \(0.519427\pi\) | |||||||
\(614\) | 21264.7 | + | 6473.49i | 1.39768 | + | 0.425487i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9865.20 | + | 25977.7i | −0.645260 | + | 1.69914i | ||||
\(617\) | −17363.4 | + | 10024.8i | −1.13294 | + | 0.654103i | −0.944673 | − | 0.328015i | \(-0.893621\pi\) |
−0.188267 | + | 0.982118i | \(0.560287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19210.5 | + | 11091.2i | 1.24739 | + | 0.720183i | 0.970589 | − | 0.240743i | \(-0.0773911\pi\) |
0.276805 | + | 0.960926i | \(0.410724\pi\) | |||||||
\(620\) | 2320.61 | − | 1138.71i | 0.150319 | − | 0.0737609i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20636.7 | − | 4790.34i | 1.33031 | − | 0.308802i | ||||
\(623\) | −2568.90 | + | 4449.46i | −0.165202 | + | 0.286138i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2694.67 | − | 4667.31i | −0.172459 | − | 0.298708i | ||||
\(626\) | 16627.4 | + | 17788.1i | 1.06161 | + | 1.13571i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 608.094 | − | 9005.44i | 0.0386395 | − | 0.572223i | ||||
\(629\) | − | 15273.1i | − | 0.968166i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28148.1i | 1.77584i | 0.459994 | + | 0.887922i | \(0.347851\pi\) | ||||
−0.459994 | + | 0.887922i | \(0.652149\pi\) | |||||||
\(632\) | −13687.0 | + | 2218.14i | −0.861452 | + | 0.139609i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11226.8 | + | 10494.3i | −0.703269 | + | 0.657382i | ||||
\(635\) | 194.191 | + | 336.348i | 0.0121358 | + | 0.0210198i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6056.53 | + | 10490.2i | −0.376716 | + | 0.652492i | ||||
\(638\) | −7982.77 | − | 34389.6i | −0.495362 | − | 2.13401i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7881.16 | − | 203.534i | 0.486766 | − | 0.0125709i | ||||
\(641\) | −6980.56 | − | 4030.23i | −0.430134 | − | 0.248338i | 0.269270 | − | 0.963065i | \(-0.413218\pi\) |
−0.699404 | + | 0.714727i | \(0.746551\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −666.166 | + | 384.611i | −0.0408570 | + | 0.0235888i | −0.520289 | − | 0.853990i | \(-0.674176\pi\) |
0.479432 | + | 0.877579i | \(0.340843\pi\) | |||||||
\(644\) | 848.193 | − | 1264.00i | 0.0518998 | − | 0.0773428i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1189.79 | + | 3908.33i | −0.0724639 | + | 0.238036i | ||||
\(647\) | −25155.2 | −1.52852 | −0.764259 | − | 0.644909i | \(-0.776895\pi\) | ||||
−0.764259 | + | 0.644909i | \(0.776895\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11508.5 | 0.696067 | ||||||||
\(650\) | 3941.47 | − | 12947.3i | 0.237842 | − | 0.781283i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8648.13 | + | 12887.7i | −0.519458 | + | 0.774114i | ||||
\(653\) | −17852.0 | + | 10306.9i | −1.06984 | + | 0.617671i | −0.928137 | − | 0.372238i | \(-0.878590\pi\) |
−0.141701 | + | 0.989910i | \(0.545257\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3384.21 | + | 1953.88i | 0.201881 | + | 0.116556i | ||||
\(656\) | 8582.62 | + | 6639.64i | 0.510815 | + | 0.395175i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1483.44 | + | 6390.65i | 0.0878886 | + | 0.378622i | ||||
\(659\) | −12082.8 | + | 20928.0i | −0.714231 | + | 1.23708i | 0.249024 | + | 0.968497i | \(0.419890\pi\) |
−0.963255 | + | 0.268587i | \(0.913443\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9976.53 | − | 17279.9i | −0.587053 | − | 1.01681i | −0.994616 | − | 0.103629i | \(-0.966955\pi\) |
0.407563 | − | 0.913177i | \(-0.366379\pi\) | |||||||
\(662\) | −3262.06 | + | 3049.22i | −0.191516 | + | 0.179020i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2049.27 | + | 12645.0i | 0.119770 | + | 0.739038i | ||||
\(665\) | 3675.84i | 0.214351i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1933.95i | 0.112268i | ||||||||
\(668\) | −1339.37 | + | 19835.2i | −0.0775777 | + | 1.14887i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10984.1 | + | 11750.9i | 0.633365 | + | 0.677575i | ||||
\(671\) | 8825.05 | + | 15285.4i | 0.507731 | + | 0.879416i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3449.60 | − | 5974.88i | 0.197581 | − | 0.342221i | −0.750162 | − | 0.661254i | \(-0.770025\pi\) |
0.947744 | + | 0.319033i | \(0.103358\pi\) | |||||||
\(674\) | 18737.2 | − | 4349.43i | 1.07082 | − | 0.248566i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2303.16 | − | 1130.15i | 0.131040 | − | 0.0643007i | ||||
\(677\) | 7812.18 | + | 4510.37i | 0.443496 | + | 0.256052i | 0.705079 | − | 0.709128i | \(-0.250911\pi\) |
−0.261584 | + | 0.965181i | \(0.584245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9810.44 | − | 5664.06i | 0.554477 | − | 0.320128i | ||||
\(680\) | −5955.44 | − | 2261.61i | −0.335854 | − | 0.127543i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8158.33 | + | 2483.59i | 0.458062 | + | 0.139445i | ||||
\(683\) | 7388.19 | 0.413911 | 0.206956 | − | 0.978350i | \(-0.433644\pi\) | ||||
0.206956 | + | 0.978350i | \(0.433644\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1200.20 | −0.0669448 | ||||||||
\(686\) | 6645.30 | + | 2022.99i | 0.369853 | + | 0.112592i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2831.16 | − | 20868.2i | 0.156885 | − | 1.15638i | ||||
\(689\) | 13068.9 | − | 7545.32i | 0.722620 | − | 0.417205i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25972.9 | − | 14995.5i | −1.42989 | − | 0.825549i | −0.432781 | − | 0.901499i | \(-0.642468\pi\) |
−0.997112 | + | 0.0759500i | \(0.975801\pi\) | |||||||
\(692\) | −10143.5 | − | 20671.7i | −0.557224 | − | 1.13558i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34319.0 | + | 7966.38i | −1.87713 | + | 0.435734i | ||||
\(695\) | 3817.95 | − | 6612.88i | 0.208378 | − | 0.360922i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4384.06 | − | 7593.41i | −0.238247 | − | 0.412656i | ||||
\(698\) | −3518.06 | − | 3763.63i | −0.190775 | − | 0.204091i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18400.9 | + | 1242.52i | 0.993554 | + | 0.0670899i | ||||
\(701\) | − | 23559.3i | − | 1.26936i | −0.772774 | − | 0.634681i | \(-0.781131\pi\) | ||
0.772774 | − | 0.634681i | \(-0.218869\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8248.82i | 0.442547i | ||||||||
\(704\) | 19453.1 | + | 17264.7i | 1.04143 | + | 0.924272i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14362.1 | − | 13425.0i | 0.765618 | − | 0.715663i | ||||
\(707\) | −21675.2 | − | 37542.6i | −1.15301 | − | 1.99708i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6114.96 | + | 10591.4i | −0.323910 | + | 0.561028i | −0.981291 | − | 0.192530i | \(-0.938331\pi\) |
0.657381 | + | 0.753558i | \(0.271664\pi\) | |||||||
\(710\) | −847.887 | − | 3652.68i | −0.0448178 | − | 0.193074i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3039.78 | + | 3726.41i | 0.160001 | + | 0.196142i | ||||
\(713\) | −404.574 | − | 233.581i | −0.0212502 | − | 0.0122688i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12017.5 | + | 6938.30i | −0.628571 | + | 0.362906i | ||||
\(716\) | −19701.6 | − | 13220.5i | −1.02833 | − | 0.690046i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −262.555 | + | 862.464i | −0.0136469 | + | 0.0448285i | ||||
\(719\) | 37718.6 | 1.95642 | 0.978211 | − | 0.207613i | \(-0.0665694\pi\) | ||||
0.978211 | + | 0.207613i | \(0.0665694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3346.11 | 0.172837 | ||||||||
\(722\) | −5007.29 | + | 16448.4i | −0.258105 | + | 0.847848i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8307.38 | − | 5574.55i | −0.426438 | − | 0.286156i | ||||
\(725\) | −20292.0 | + | 11715.6i | −1.03949 | + | 0.600147i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7555.48 | + | 4362.16i | 0.385443 | + | 0.222536i | 0.680184 | − | 0.733041i | \(-0.261900\pi\) |
−0.294741 | + | 0.955577i | \(0.595233\pi\) | |||||||
\(728\) | 17349.3 | + | 21268.2i | 0.883252 | + | 1.08276i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3811.38 | − | 16419.4i | −0.193241 | − | 0.832476i | ||||
\(731\) | −8508.39 | + | 14737.0i | −0.430498 | + | 0.745645i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7960.97 | + | 13788.8i | 0.401153 | + | 0.694817i | 0.993865 | − | 0.110597i | \(-0.0352762\pi\) |
−0.592712 | + | 0.805414i | \(0.701943\pi\) | |||||||
\(734\) | −12944.2 | + | 12099.6i | −0.650923 | + | 0.608452i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −824.189 | − | 1162.22i | −0.0412772 | − | 0.0582065i | ||||
\(737\) | 53066.9i | 2.65230i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 21026.0i | − | 1.04662i | −0.852141 | − | 0.523312i | \(-0.824696\pi\) | ||
0.852141 | − | 0.523312i | \(-0.175304\pi\) | |||||||
\(740\) | −12833.2 | − | 866.565i | −0.637511 | − | 0.0430480i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14042.7 | + | 15022.9i | 0.694774 | + | 0.743271i | ||||
\(743\) | 5813.11 | + | 10068.6i | 0.287029 | + | 0.497148i | 0.973099 | − | 0.230387i | \(-0.0739992\pi\) |
−0.686071 | + | 0.727535i | \(0.740666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4052.60 | − | 7019.32i | 0.199297 | − | 0.345192i | ||||
\(746\) | −33426.8 | + | 7759.27i | −1.64054 | + | 0.380814i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9258.24 | − | 18867.6i | −0.452560 | − | 0.922284i | ||||
\(749\) | 16147.6 | + | 9322.82i | 0.787744 | + | 0.454804i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6096.06 | − | 3519.56i | 0.296203 | − | 0.171013i | −0.344533 | − | 0.938774i | \(-0.611963\pi\) |
0.640736 | + | 0.767761i | \(0.278629\pi\) | |||||||
\(752\) | 6084.95 | + | 825.539i | 0.295074 | + | 0.0400323i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33359.3 | − | 10155.4i | −1.61124 | − | 0.490500i | ||||
\(755\) | −10712.8 | −0.516395 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28354.3 | −1.36137 | −0.680685 | − | 0.732577i | \(-0.738318\pi\) | ||||
−0.680685 | + | 0.732577i | \(0.738318\pi\) | |||||||
\(758\) | −5218.77 | − | 1588.72i | −0.250072 | − | 0.0761279i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3216.47 | + | 1221.47i | 0.153518 | + | 0.0582994i | ||||
\(761\) | 20274.5 | − | 11705.5i | 0.965771 | − | 0.557588i | 0.0678265 | − | 0.997697i | \(-0.478394\pi\) |
0.897944 | + | 0.440109i | \(0.145060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5773.51 | − | 3333.34i | −0.273939 | − | 0.158158i | ||||
\(764\) | −5569.79 | + | 2733.07i | −0.263754 | + | 0.129423i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16392.9 | − | 3805.24i | 0.773237 | − | 0.179490i | ||||
\(767\) | 5683.65 | − | 9844.37i | 0.267568 | − | 0.463441i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12632.8 | + | 21880.6i | 0.592392 | + | 1.02605i | 0.993909 | + | 0.110202i | \(0.0351498\pi\) |
−0.401517 | + | 0.915852i | \(0.631517\pi\) | |||||||
\(770\) | −12912.9 | − | 13814.3i | −0.604350 | − | 0.646535i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2356.08 | − | 34891.9i | 0.109841 | − | 1.62667i | ||||
\(773\) | − | 31081.3i | − | 1.44621i | −0.690740 | − | 0.723103i | \(-0.742715\pi\) | ||
0.690740 | − | 0.723103i | \(-0.257285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5660.02i | − | 0.262340i | ||||||
\(776\) | −1696.24 | − | 10466.6i | −0.0784682 | − | 0.484186i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4827.00 | − | 4512.05i | 0.222438 | − | 0.207924i | ||||
\(779\) | 2367.78 | + | 4101.12i | 0.108902 | + | 0.188624i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6185.49 | − | 10713.6i | 0.283399 | − | 0.490861i | ||||
\(782\) | 260.325 | + | 1121.47i | 0.0119043 | + | 0.0512837i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9453.75 | + | 12220.2i | −0.430656 | + | 0.556679i | ||||
\(785\) | 5319.29 | + | 3071.09i | 0.241852 | + | 0.139633i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29654.1 | + | 17120.8i | −1.34314 | + | 0.775463i | −0.987267 | − | 0.159070i | \(-0.949150\pi\) |
−0.355875 | + | 0.934534i | \(0.615817\pi\) | |||||||
\(788\) | −7348.92 | + | 10951.6i | −0.332227 | + | 0.495095i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2747.90 | − | 9026.54i | 0.123754 | − | 0.406519i | ||||
\(791\) | 15155.2 | 0.681233 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17433.6 | 0.780686 | ||||||||
\(794\) | 5008.34 | − | 16451.9i | 0.223853 | − | 0.735333i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13134.2 | − | 19573.0i | 0.584836 | − | 0.871542i | ||||
\(797\) | 15734.1 | − | 9084.08i | 0.699285 | − | 0.403732i | −0.107796 | − | 0.994173i | \(-0.534379\pi\) |
0.807081 | + | 0.590441i | \(0.201046\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4297.16 | − | 2480.96i | −0.190266 | − | 0.109850i | ||||
\(800\) | 7201.81 | − | 15688.4i | 0.318278 | − | 0.693337i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8860.21 | + | 38169.6i | 0.390106 | + | 1.68057i | ||||
\(803\) | 27804.8 | − | 48159.2i | 1.22193 | − | 2.11644i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 517.936 | + | 897.092i | 0.0226768 | + | 0.0392774i | ||||
\(806\) | 6153.59 | − | 5752.08i | 0.268922 | − | 0.251375i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −40053.5 | + | 6491.15i | −1.74391 | + | 0.282621i | ||||
\(809\) | − | 24608.1i | − | 1.06944i | −0.845029 | − | 0.534720i | \(-0.820417\pi\) | ||
0.845029 | − | 0.534720i | \(-0.179583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3293.86i | 0.142618i | 0.997454 | + | 0.0713089i | \(0.0227176\pi\) | ||||
−0.997454 | + | 0.0713089i | \(0.977282\pi\) | |||||||
\(812\) | 3201.42 | − | 47410.8i | 0.138359 | − | 2.04900i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28977.4 | − | 31000.1i | −1.24774 | − | 1.33483i | ||||
\(815\) | −5280.85 | − | 9146.70i | −0.226969 | − | 0.393123i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4595.30 | − | 7959.29i | 0.196780 | − | 0.340833i | ||||
\(818\) | −746.295 | + | 173.236i | −0.0318993 | + | 0.00740470i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6629.12 | + | 3252.88i | −0.282316 | + | 0.138531i | ||||
\(821\) | 33264.9 | + | 19205.5i | 1.41407 | + | 0.816414i | 0.995769 | − | 0.0918946i | \(-0.0292923\pi\) |
0.418301 | + | 0.908308i | \(0.362626\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −531.302 | + | 306.747i | −0.0225031 | + | 0.0129922i | −0.511209 | − | 0.859456i | \(-0.670802\pi\) |
0.488706 | + | 0.872448i | \(0.337469\pi\) | |||||||
\(824\) | 1111.91 | − | 2927.95i | 0.0470086 | − | 0.123786i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14818.8 | + | 4511.21i | 0.624229 | + | 0.190031i | ||||
\(827\) | −19933.1 | −0.838140 | −0.419070 | − | 0.907954i | \(-0.637644\pi\) | ||||
−0.419070 | + | 0.907954i | \(0.637644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32209.0 | 1.34941 | 0.674707 | − | 0.738086i | \(-0.264270\pi\) | ||||
0.674707 | + | 0.738086i | \(0.264270\pi\) | |||||||
\(830\) | −8339.37 | − | 2538.71i | −0.348751 | − | 0.106168i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24375.5 | − | 8113.78i | 1.01571 | − | 0.338094i | ||||
\(833\) | 10811.8 | − | 6242.17i | 0.449706 | − | 0.259638i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11716.1 | − | 6764.32i | −0.485573 | − | 0.280346i | ||||
\(836\) | 5000.28 | + | 10190.2i | 0.206864 | + | 0.421574i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21770.0 | + | 5053.41i | −0.897413 | + | 0.208314i | ||||
\(839\) | −21916.3 | + | 37960.1i | −0.901828 | + | 1.56201i | −0.0767097 | + | 0.997053i | \(0.524441\pi\) |
−0.825119 | + | 0.564959i | \(0.808892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17991.3 | + | 31161.9i | 0.737682 | + | 1.27770i | ||||
\(842\) | 12870.9 | + | 13769.3i | 0.526792 | + | 0.563564i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4397.14 | + | 296.918i | 0.179332 | + | 0.0121094i | ||||
\(845\) | 1745.83i | 0.0710750i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30208.9i | − | 1.22549i | ||||||
\(848\) | 17811.8 | − | 7295.69i | 0.721297 | − | 0.295442i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10190.1 | + | 9525.22i | −0.411197 | + | 0.384368i | ||||
\(851\) | 1162.28 | + | 2013.13i | 0.0468184 | + | 0.0810919i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6391.08 | + | 11069.7i | −0.256537 | + | 0.444336i | −0.965312 | − | 0.261099i | \(-0.915915\pi\) |
0.708775 | + | 0.705435i | \(0.249248\pi\) | |||||||
\(854\) | 5371.79 | + | 23141.6i | 0.215245 | + | 0.927269i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13523.6 | − | 11031.7i | 0.539983 | − | 0.440485i | ||||
\(857\) | −32179.0 | − | 18578.6i | −1.28263 | − | 0.740527i | −0.305302 | − | 0.952256i | \(-0.598757\pi\) |
−0.977329 | + | 0.211728i | \(0.932091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7232.93 | + | 4175.93i | −0.287293 | + | 0.165869i | −0.636720 | − | 0.771095i | \(-0.719709\pi\) |
0.349428 | + | 0.936963i | \(0.386376\pi\) | |||||||
\(860\) | 11900.0 | + | 7985.34i | 0.471846 | + | 0.316626i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12168.8 | − | 39973.1i | 0.480824 | − | 1.57945i | ||||
\(863\) | −11795.5 | −0.465265 | −0.232633 | − | 0.972565i | \(-0.574734\pi\) | ||||
−0.232633 | + | 0.972565i | \(0.574734\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15669.5 | 0.615929 | ||||||||
\(866\) | 1954.53 | − | 6420.41i | 0.0766947 | − | 0.251934i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9531.49 | + | 6395.97i | 0.372719 | + | 0.250108i | ||||
\(869\) | 26958.4 | − | 15564.4i | 1.05236 | − | 0.607580i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45393.5 | + | 26207.9i | 1.76590 | + | 1.01954i | ||||
\(872\) | −4835.29 | + | 3944.33i | −0.187780 | + | 0.153179i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −140.599 | − | 605.697i | −0.00544145 | − | 0.0234416i | ||||
\(875\) | −14500.6 | + | 25115.8i | −0.560240 | + | 0.970364i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7828.97 | + | 13560.2i | 0.301443 | + | 0.522114i | 0.976463 | − | 0.215685i | \(-0.0691984\pi\) |
−0.675020 | + | 0.737799i | \(0.735865\pi\) | |||||||
\(878\) | −5987.63 | + | 5596.95i | −0.230151 | + | 0.215134i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16378.8 | + | 6708.74i | −0.627421 | + | 0.256991i | ||||
\(881\) | 39103.2i | 1.49537i | 0.664054 | + | 0.747684i | \(0.268834\pi\) | ||||
−0.664054 | + | 0.747684i | \(0.731166\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23664.8i | 0.901907i | 0.892547 | + | 0.450953i | \(0.148916\pi\) | ||||
−0.892547 | + | 0.450953i | \(0.851084\pi\) | |||||||
\(884\) | −20711.7 | − | 1398.56i | −0.788020 | − | 0.0532112i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15189.2 | − | 16249.4i | −0.575949 | − | 0.616152i | ||||
\(887\) | 22019.4 | + | 38138.8i | 0.833529 | + | 1.44371i | 0.895223 | + | 0.445619i | \(0.147016\pi\) |
−0.0616939 | + | 0.998095i | \(0.519650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −862.316 | + | 1493.58i | −0.0325322 | + | 0.0563475i | ||||
\(890\) | −3187.78 | + | 739.970i | −0.120061 | + | 0.0278695i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6367.77 | + | 12977.1i | 0.239023 | + | 0.487112i | ||||
\(893\) | 2320.85 | + | 1339.94i | 0.0869701 | + | 0.0502122i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13982.7 | − | 8072.89i | 0.522222 | − | 0.301505i | ||||
\(896\) | 18281.1 | + | 29856.2i | 0.681618 | + | 1.11320i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3614.73 | + | 1100.41i | 0.134326 | + | 0.0408922i | ||||
\(899\) | −14583.3 | −0.541024 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15553.2 | −0.575086 | ||||||||
\(902\) | −23305.3 | − | 7094.70i | −0.860291 | − | 0.261893i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5036.02 | − | 13261.2i | 0.185283 | − | 0.487900i | ||||
\(905\) | 5895.93 | − | 3404.02i | 0.216561 | − | 0.125031i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28310.7 | + | 16345.2i | 1.03643 | + | 0.598384i | 0.918820 | − | 0.394676i | \(-0.129143\pi\) |
0.117610 | + | 0.993060i | \(0.462477\pi\) | |||||||
\(908\) | 10813.1 | − | 5305.93i | 0.395204 | − | 0.193925i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18194.0 | + | 4223.33i | −0.662775 | + | 0.153848i | ||||
\(911\) | 12749.9 | − | 22083.5i | 0.463693 | − | 0.803140i | −0.535448 | − | 0.844568i | \(-0.679857\pi\) |
0.999141 | + | 0.0414281i | \(0.0131907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14379.5 | − | 24906.1i | −0.521241 | − | 0.902817i | ||||
\(914\) | −33593.7 | − | 35938.7i | −1.21574 | − | 1.30060i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −826.802 | + | 12244.4i | −0.0298235 | + | 0.441665i | ||||
\(917\) | 17352.6i | 0.624901i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20221.1i | − | 0.725825i | −0.931823 | − | 0.362912i | \(-0.881782\pi\) | ||
0.931823 | − | 0.362912i | \(-0.118218\pi\) | |||||||
\(920\) | 957.091 | − | 155.108i | 0.0342982 | − | 0.00555844i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4612.33 | + | 4311.38i | −0.164749 | + | 0.154000i | ||||
\(923\) | −6109.61 | − | 10582.2i | −0.217877 | − | 0.377374i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14081.9 | + | 24390.6i | −0.500551 | + | 0.866980i | ||||
\(926\) | 2537.42 | + | 10931.2i | 0.0900485 | + | 0.387927i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40422.0 | − | 18555.8i | −1.42987 | − | 0.656385i | ||||
\(929\) | −32318.8 | − | 18659.3i | −1.14139 | − | 0.658979i | −0.194612 | − | 0.980880i | \(-0.562345\pi\) |
−0.946773 | + | 0.321901i | \(0.895678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5839.32 | + | 3371.33i | −0.205560 | + | 0.118680i | ||||
\(932\) | 5603.49 | − | 8350.50i | 0.196940 | − | 0.293487i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7257.13 | + | 23838.9i | −0.254241 | + | 0.835152i | ||||
\(935\) | 14301.9 | 0.500239 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16237.5 | −0.566121 | −0.283060 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283060 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(938\) | −20801.7 | + | 68331.3i | −0.724094 | + | 2.37857i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2328.45 | + | 3469.93i | −0.0807932 | + | 0.120401i | ||||
\(941\) | 1785.15 | − | 1030.66i | 0.0618429 | − | 0.0357050i | −0.468760 | − | 0.883326i | \(-0.655299\pi\) |
0.530603 | + | 0.847621i | \(0.321966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1155.72 | + | 667.254i | 0.0399102 | + | 0.0230422i | ||||
\(944\) | 8871.72 | − | 11467.9i | 0.305879 | − | 0.395389i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10690.6 | + | 46054.9i | 0.367422 | + | 1.58285i | ||||
\(947\) | 8954.48 | − | 15509.6i | 0.307267 | − | 0.532202i | −0.670497 | − | 0.741913i | \(-0.733919\pi\) |
0.977763 | + | 0.209711i | \(0.0672523\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27463.6 | − | 47568.4i | −0.939418 | − | 1.62712i | ||||
\(950\) | 5503.57 | − | 5144.47i | 0.187957 | − | 0.175693i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4525.41 | − | 27923.9i | −0.154064 | − | 0.950651i | ||||
\(953\) | − | 10905.6i | − | 0.370689i | −0.982674 | − | 0.185344i | \(-0.940660\pi\) | ||
0.982674 | − | 0.185344i | \(-0.0593400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4221.99i | − | 0.143058i | ||||||
\(956\) | −988.459 | + | 14638.4i | −0.0334404 | + | 0.495229i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37601.5 | + | 40226.2i | 1.26811 | + | 1.35663i | ||||
\(959\) | −2664.78 | − | 4615.53i | −0.0897291 | − | 0.155415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13134.1 | + | 22749.0i | −0.440876 | + | 0.763619i | ||||
\(962\) | −40828.4 | + | 9477.40i | −1.36836 | + | 0.317634i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5153.35 | − | 2528.72i | 0.172177 | − | 0.0844862i | ||||
\(965\) | 20609.8 | + | 11899.0i | 0.687515 | + | 0.396937i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42102.8 | + | 24308.1i | −1.40014 | + | 0.808370i | −0.994406 | − | 0.105622i | \(-0.966317\pi\) |
−0.405732 | + | 0.913992i | \(0.632983\pi\) | |||||||
\(968\) | −26433.7 | − | 10038.4i | −0.877699 | − | 0.333311i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6902.70 | + | 2101.35i | 0.228487 | + | 0.0695570i | ||||
\(971\) | −24102.8 | −0.796596 | −0.398298 | − | 0.917256i | \(-0.630399\pi\) | ||||
−0.398298 | + | 0.917256i | \(0.630399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33907.7 | 1.11719 | ||||||||
\(974\) | −14141.3 | − | 4304.97i | −0.465213 | − | 0.141622i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22034.6 | + | 2989.41i | 0.722654 | + | 0.0980417i | ||||
\(977\) | −21356.3 | + | 12330.1i | −0.699333 | + | 0.403760i | −0.807099 | − | 0.590416i | \(-0.798964\pi\) |
0.107766 | + | 0.994176i | \(0.465630\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9349.99 | − | 5398.22i | −0.305237 | − | 0.176229i | ||||
\(980\) | −4631.56 | − | 9438.77i | −0.150969 | − | 0.307664i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26414.2 | − | 6131.46i | 0.858361 | − | 0.199249i | ||||
\(983\) | −11000.9 | + | 19054.2i | −0.356943 | + | 0.618244i | −0.987449 | − | 0.157941i | \(-0.949514\pi\) |
0.630505 | + | 0.776185i | \(0.282848\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4487.51 | − | 7772.59i | −0.145161 | − | 0.251427i | ||||
\(986\) | 24542.2 | + | 26255.3i | 0.792681 | + | 0.848012i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11186.2 | + | 755.348i | 0.360202 | + | 0.0243227i | ||||
\(989\) | − | 2589.96i | − | 0.0832718i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 21100.2i | − | 0.676358i | −0.941082 | − | 0.338179i | \(-0.890189\pi\) | ||
0.941082 | − | 0.338179i | \(-0.109811\pi\) | |||||||
\(992\) | 8763.96 | − | 6214.97i | 0.280500 | − | 0.198917i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12164.3 | − | 11370.6i | 0.388159 | − | 0.362832i | ||||
\(995\) | 8020.20 | + | 13891.4i | 0.255535 | + | 0.442600i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4141.70 | + | 7173.64i | −0.131564 | + | 0.227875i | −0.924280 | − | 0.381716i | \(-0.875333\pi\) |
0.792716 | + | 0.609591i | \(0.208666\pi\) | |||||||
\(998\) | 1540.23 | + | 6635.30i | 0.0488530 | + | 0.210458i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.4.h.b.35.5 | 24 | ||
3.2 | odd | 2 | 36.4.h.b.11.8 | yes | 24 | ||
4.3 | odd | 2 | inner | 108.4.h.b.35.10 | 24 | ||
9.2 | odd | 6 | 324.4.b.c.323.4 | 24 | |||
9.4 | even | 3 | 36.4.h.b.23.3 | yes | 24 | ||
9.5 | odd | 6 | inner | 108.4.h.b.71.10 | 24 | ||
9.7 | even | 3 | 324.4.b.c.323.21 | 24 | |||
12.11 | even | 2 | 36.4.h.b.11.3 | ✓ | 24 | ||
36.7 | odd | 6 | 324.4.b.c.323.3 | 24 | |||
36.11 | even | 6 | 324.4.b.c.323.22 | 24 | |||
36.23 | even | 6 | inner | 108.4.h.b.71.5 | 24 | ||
36.31 | odd | 6 | 36.4.h.b.23.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.3 | ✓ | 24 | 12.11 | even | 2 | ||
36.4.h.b.11.8 | yes | 24 | 3.2 | odd | 2 | ||
36.4.h.b.23.3 | yes | 24 | 9.4 | even | 3 | ||
36.4.h.b.23.8 | yes | 24 | 36.31 | odd | 6 | ||
108.4.h.b.35.5 | 24 | 1.1 | even | 1 | trivial | ||
108.4.h.b.35.10 | 24 | 4.3 | odd | 2 | inner | ||
108.4.h.b.71.5 | 24 | 36.23 | even | 6 | inner | ||
108.4.h.b.71.10 | 24 | 9.5 | odd | 6 | inner | ||
324.4.b.c.323.3 | 24 | 36.7 | odd | 6 | |||
324.4.b.c.323.4 | 24 | 9.2 | odd | 6 | |||
324.4.b.c.323.21 | 24 | 9.7 | even | 3 | |||
324.4.b.c.323.22 | 24 | 36.11 | even | 6 |